ΜΕ12 | Computational Methods for Energy Problems

Postgraduate Study Program | Power Systems

Classification of Partial Differential Equations. The Finite Difference Method. Finite Difference Solution of the Laplace Equation. Iterative Methods of Solution. Parabolic Partial Differential Equations. Features of Parabolic PDEs. The Forward-Time Centered-Space (FTCS) Method. Consistency, Order, Stability, and Convergence. Implicit Methods. The Backward-Time Centered-Space (BTCS) Method. The Crank Nicolson Method. Hyperbolic Partial Differential Equations. General Features of Hyperbolic. The Forward-Time Centered-Space (FTCS) Method, Upwind Method and the Lax Method. The Wave Equation. Nonlinear Equations and Multidimensional Problems. Conservative form and Global Conservation Property. Velocity – Pressure Coupling in Incompressible Flows, SIMPLE and PISO methods, Rhie and Chow Technique. Finite Volumes Method. Finite Volume Grid. Volume and Surface Integrals.